A process on a machine has a standard deviation of 0.04 inches. If a product with specifications of /- 0.07 inches has to be processed on that machine, is the machine capable of performing that job

No, it can't perform because C_p < 1

Step-by-step explanation:

We are told that a product with specifications of ± 0.07 inches has to be processed on that machine. This means that the product is centered on the machine.

Thus;

Specification Width = 2 × 0.07 = 0.14

Now, formula for capability index is;

C_p = specification width/(6 × standard deviation)

We are given standard deviation = 0.04. Thus;

C_p = 0.14/(6 × 0.04)

C_p = 0.5833

Now, for this process, C_p should not be less than 1. However in this case it is less than 1,thus it means that the machine will not be able to perform the job.

We can solve these equations by using substitution method where you substitute one equation to the other and solve for the value of the other variable. We do as follows:

y = 2x^2
y = –3x −1

 2x^2 = –3x −1
 2x^2 +3x +1 = 0

x1= -0.5
x2 = -1
y1 = 0.5
y2 = 2